A Translation and Study of a Hellenistic Treatise in Spherical Astronomy

Author: Euclid,J. L. Berggren,Robert S. D. Thomas

Publisher: American Mathematical Soc.

ISBN: 082184072X

Category: Mathematics

Page: 132

View: 2676

This book contains a translation and study of ""Euclid's Phaenomena"", a work which once formed part of the mathematical training of astronomers from Central Asia to Western Europe. Included is an introduction that sets Euclid's geometry of the celestial sphere, and its application to the astronomy of his day, into its historical context for readers not already familiar with it. So no knowledge of astronomy or advanced mathematics is necessary for an understanding of the work. The book shows mathematical astronomy shortly before the invention of trigonometry, which allowed the calculation of exact results and the subsequent composition of ""Ptolemy's Almagest"".""The Phaenomena"" itself begins with an introduction (possibly not by Euclid) followed by eighteen propositions set out in geometrical style about how arcs of the zodiacal circle move across the sky. The astronomical application is to the small arc of that circle occupied by the Sun, but the Sun is not mentioned. This work and the (roughly) contemporaneous treatises of Autolycus and Aristarchos form a corpus of the oldest extant works on mathematical astronomy. Together with ""Euclid's Optics"", one has the beginnings of the history of science as an application of mathematics.
Posted in Mathematics

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Posted in Mathematics

Since man first looked towards the heavens, a great deal of effort has been put into trying to predict and explain the motions of the sun, moon and planets. Developments in man's understanding have been closely linked to progress in the mathematical sciences. Whole new areas of mathematics, such as trigonometry, were developed to aid astronomical calculations, and on numerous occasions throughout history, breakthroughs in astronomy have only been possible because of progress in mathematics. This book describes the theories of planetary motion that have been developed through the ages, beginning with the homocentric spheres of Eudoxus and ending with Einstein's general theory of relativity. It emphasizes the interaction between progress in astronomy and in mathematics, showing how the two have been inextricably linked since Babylonian times. This valuable text is accessible to a wide audience, from amateur astronomers to professional historians of astronomy.
Posted in Science

A Study of Bibliography and the Book Trade in Relation to the History of Science

Author: Andrew Hunter

Publisher: Routledge

ISBN: 1351878956

Category: Literary Criticism

Page: 424

View: 6840

In the 25 years since the last edition of Thornton and Tully’s Scientific Books, Libraries and Collectors was published, scientific publishing has mushroomed, developed new forms, and the academic discipline and popular appreciation of the history of science have grown apace. This fourth edition discusses these changes and ponders the implications of developments in publishing at the end of the twentieth century, while concentrating its gaze upon the dissemination of scientific ideas and knowledge from Antiquity to the industrial age. In this shift of focus it departs from previous editions, and for the first time a chapter on Islamic science is included. Recurrent themes in several of the ten essays in the present volume are the definition of ’science’ itself, and its transmutation by publishing media and the social context. Two essays on the collecting of scientific books provide a counterpoint, and the book is grounded on a rigorous chapter on bibliographies. The timely publication of Scientific Books, Libraries and Collectors comes at the coincidence of the advent of electronic publishing and the millennium, a dramatic moment at which to take stock.
Posted in Literary Criticism

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Posted in Reference

The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VIVII of Platos Republic and Aristotles Prior and Posterior Analytics, to Kants Critique of Pure Reason and Mills A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 19011950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors.
Posted in Philosophy

all thirteen books complete in one volume : the Thomas L. Heath translation

Author: Euclid,Dana Densmore

Publisher: Green Lion Pr

ISBN: N.A

Category: Mathematics

Page: 499

View: 1787

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.
Posted in Mathematics